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A158506 Determinants of n-times-n matrices M of the form M[i,j] = 2^(i*j). 0

%I #6 Apr 17 2018 03:31:44

%S 2,16,3072,66060288,681869007912960,13963783542711369125068800,

%T 2305981313752949175455638153064349696000,

%U 12380897999371387785024422461502386865911933091803299840000

%N Determinants of n-times-n matrices M of the form M[i,j] = 2^(i*j).

%F a(n)=2^((1/6)*n*(n+1)*(n+2))*product(product(2^p-1, p = 1..l), l = 1..n-1).

%F a(n)=2^A000292(n)*product_{i=1..n-1} A005329(i). - _R. J. Mathar_, Mar 27 2009

%F a(n) ~ c * QPochhammer(1/2)^n * 2^(n*(2*n^2 + 3*n + 1)/6), where c = 10.032129775337715051413862095841451215826928327290198829... - _Vaclav Kotesovec_, Apr 17 2018

%p a(n) := 2^((1/6)*n*(n+1)*(n+2))*mul(mul(2^p-1, p = 1..l), l = 1..n-1):

%t Table[2^(n*(n+1)*(n+2)/6) * Product[Product[2^p-1, {p,1,m}], {m,1,n-1}], {n,1,10}] (* _Vaclav Kotesovec_, Apr 17 2018 *)

%K nonn

%O 1,1

%A P. Dunin-Barkowski, A. Sleptsov (elandread(AT)yandex.ru), Mar 20 2009

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Last modified July 19 01:31 EDT 2024. Contains 374388 sequences. (Running on oeis4.)